How to make irregular Honey Comb
In a regular triangulation of a regular quad topology, vertices connect six edges, and its Dual is a hexagonal mesh..

So as @Leander has hinted in the commentary .. 


Install the shipped 'Tissue' Add-on
CtrlT or use the modifier to triangulate the mesh
Use one of the Add-on's 'Dual' operations.




The regions of the mesh which were quad grids will become hexagonal grids.